Avian polygyny is most likely in populations with high variability in heritable male fitness

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Abstract
In all mating systems where males can gain more than one female (including lekking), males expend effort on attracting mates at the expense of parental effort. Previous theoretical work concluded that, when opportunities for additional matings are high, males should forgo investment in a current clutch. However, in most avian species, opportunities for additional matings occur when more than one female chooses to mate with an individual male. Thus polygyny occurs as a result of female choice. Any general explanation for the evolution of polygyny must also include a discussion of why females choose to mate with a male who invests in mating effort at the expense of his investment in her offspring. Here we show, by using a joint evolutionarily stable strategy (ESS) model, that male investment in display and female choice for displaying males are evolutionarily stable when the `good genes' advantage of female choice is large enough to outweigh the loss of paternal care. We also show that the `good genes' advantage for choice is significant only when there is sufficient variation in the quality of males. If there is little variation amongst males, high-quality males chosen by choosy females will only be slightly better than average ones. Thus there will be little benefit to offset the cost of lost parental care for choosy females, and the benefit for male display will be low. The invasion and stability conditions for female choice and male display are satisfied when male genetic quality is highly variable. Therefore we predict that polygynous mating systems are most likely in populations and species in which there is high heritable variation in male genetic quality.